Keywords: Control of networks, Decentralized control, Agents-based systems
Abstract: Cohesive networks aim to achieve similar response in each agent not only at steady state but also during transitions from one consensus value to another. Standard consensus-based approaches approximate the diffusion equation, which leads to decay of transition information for agents that are farther away from the leader, and results in loss of cohesion during rapid changes. Increasing the alignment strength in standard first-order consensus-based approaches enables each agent to respond faster to the changes in neighbor states. Nevertheless, it does not necessarily increase cohesion during the transition. Moreover, increasing the alignment strength also requires an increase in update bandwidth. In contrast, delayed self reinforcement (DSR) approach enables increased cohesion without increasing the update bandwidth. The main contribution of this article is to explain this increased cohesion with DSR by showing that the DSR approximates a strongly damped wave equation, where each agent not only attempts to align with its neighboring states but also to align with the rate of change of its neighboring states.

Keywords: Machine learning, Identification, Optimization
Abstract: Optimization of industrial continuous casting process requires faster models tuned across various operating regimes. Data based modelling techniques like Support Vector Regression (SVR) are proven to be efficient modelling techniques as they are based on structural risk minimization principle. However, the hyper-parameters of SVR are usually tuned on trial-and-error basis without any rationale leading to inappropriate model. To generate an efficient model for the continuous casting process, we propose an algorithm for estimating the hyper-parameters of SVR by considering Root Mean Square Error (RMSE) of the model and sample size required for modelling as the conflicting objectives. Differing importance to various inputs under different conditions leads us to use different kernel parameters for different inputs during model development. Additionally, many kernels are explored to decipher the unknown nature of the continuous casting process. Simulation results show that the proposed algorithm could develop temperature and bulging models, with which the optimization of the casting process has been shown to be effective.

Keywords: Iterative learning control, Indirect adaptive control, Optimization
Abstract: In this paper, we present a two-tier approach to achieve faster convergence in the presence of parameter uncertainties for discrete-time Iterative Learning Control (ILC) systems. The Multiple-Models with Second-Level Adaptation (MM-SLA) methodology is presented to minimize the time taken for tracking error to converge. The advantages of such an approach have not been exploited thus far in the context of adaptive ILC (AILC). We show here that AILC with MM-SLA leads to a significant reduction in the control energy besides faster convergence in the tracking error. Using simulation examples, we demonstrate the efficacy of the proposed strategies.

Keywords: Biomedical, Neural networks, Machine learning
Abstract: Science and technology has had a huge impact in the field of medicine leading to more accurate and preventive diagnosis, and treatment. Detecting brain tumors in early stages is essential for timely treatment of patients. Automatic segmentation of brain tumors is a challenging task as tumors vary in shapes and size. In this paper, we propose a fully automatic novel deep learning architecture for brain tumor segmentation named ATSNet. The network provides an end-to-end solution for feature extraction and brain tumor segmentation on Magnetic Resonance Images. Our proposed model uses an encoder-decoder architecture, employing residual modules for tackling gradient dispersion and uses skip connections for better feature map synthesis. The network utilizes attention gates (AG) to tackle the variability of brain tumors. Performance metrics such as dice score, precision, recall and intersection-over-union (IoU) have been used to evaluate and benchmark our model against those reported in literature. We have evaluated our model using the k-fold cross-validation approach. Our analysis also includes an ablation study on our model to identify important parts of the architecture by their effect on performance for optimizing the model.

Keywords: Finance, Stochastic systems
Abstract: In an earlier contribution “Unconstrained hedging within a regime-switching market model” the authors address the problem of unconstrained hedging in a financial market model which includes regime-switching, in the sense that the basic sources of randomness in the market model are a standard multidimensional Brownian motion, together with an independent finite-state Markov chain (the latter process models so-called regime-switches, which are occasional large scale random changes in the market parameters, as opposed to the persistent small scale changes in the market parameters which are driven by the Brownian motion). Under these conditions the market model is incomplete, and the best that one can do is establish existence of a least initial wealth along with an investment strategy for which the corresponding wealth process almost-surely majorizes - but generally does not equal - the contingent claim at close of trade (in this case the claim is said to be super-hedged). The goal of the present work is to complement this result and introduce natural conditions on the regime-switching model under which there exists a least initial wealth and an investment strategy such that the corresponding wealth almost-surely equals the contingent claim at close of trade. Our motivation is primarily in the works of Cvitanic and Karatzas and El Karoui and Quenez who address the case where incompleteness in the market model arises from portfolio constraints rather than regime-switching.

Keywords: Filtering, Chaotic systems
Abstract: Particle filters and ensemble Kalman filters are widely used in data assimilation but in the case of deterministic systems, which are quite commonly used in earth science applications, only a few theoretical results for their stability are available. Current numerical literature explores stability in terms of RMSE which, although practical, can not represent the distance between probability measures, convergence of which is what defines filter stability. In this study, we explore the distance between filtering distributions starting from different initial distributions as a function of time using Wasserstein metric, thus directly assessing the stability of these filters. These experiments are conducted on the chaotic Lorenz-63 and Lorenz-96 models for various initial distributions for particle and ensemble Kalman filters. We show that even in cases when both these filters are stable, the filtering distributions given by each of them may be distinct.

Keywords: Optimal control, Stochastic systems
Abstract: This paper build on our recent work where we presented a dual stochastic optimal control formulation of the nonlinear filtering problem [1]. The constraint for the dual problem is a backward stochastic differential equations (BSDE). The solution is obtained via an application of the maximum principle (MP). In the present paper, a dynamic programming (DP) principle is presented for a special class of BSDE-constrained stochastic optimal control problems. The principle is applied to derive the solution of the nonlinear filtering problem.

Keywords: Machine learning, Stochastic systems, Optimal control
Abstract: We present a method to find a cost-optimal policy for a given finite-horizon Markov decision process (MDP) with unknown transition probability, such that the probability of satisfying a given signal temporal logic specification is above a desired threshold. We propose an augmentation of the MDP state space to enable the expression of the STL objective as a reachability objective. In this augmented space, the optimal policy problem is re-formulated as a finite-horizon constrained Markov decision process (CMDP). We then develop a model-free reinforcement learning (RL) scheme to provide an approximately optimal policy for any general finite horizon CMDP problem. This scheme can make use of any off-the-shelf model-free RL algorithm and considers the general space of non-stationary randomized policies. Finally, we illustrate the applicability of our RL-based approach through two case studies.

Keywords: Control applications, Nonlinear systems, Aerospace
Abstract: In this paper, a novel fully quaternion-based nonlinear dynamic inversion (NDI) controller is developed for attitude tracking of a rigid body in mathds{R}^3. Such a nonlinear controller finds its application in highly maneuverable systems such as satellites and quadrotors. The quaternion-based control avoids gimbal lock problem associated with Euler angles and allows almost global asymptotic stability. The attitude controller is well suited for rigid body systems like satellites which require minimising large-angle errors. Extensive simulations are performed on MATLAB to validate the proposed ideas and provide a comparison with existing works. A realistic physics-engine-based simulation is carried out in Gazebo to validate the proposed methodology on a quadrotor.

Keywords: Spacecraft control, Multivehicle systems, Cooperative control
Abstract: It is well acknowledged that human-made technology is not always at par with human curiosity, and an example is the inability to send large telescopes to outer space despite their higher resolution and less atmospheric interference. In this paper, we develop a framework for autonomous in-orbit construction using spacecraft formation such that a large telescope can be built in an elliptic orbit using multiple spacecraft. We split this problem into four steps for converging the position and attitude of each spacecraft at predefined values around a central spacecraft. Each spacecraft performs attitude synchronization with its neighbors to match its three degrees of freedom in orientation as a parabolic mirror. Simulations validate our proposed methods and the paper concludes with an open possibility of using other techniques to improve upon existing results.

Keywords: Machine learning, Mechanical systems/robotics, Simulation
Abstract: Mobile manipulators consist of a ground robot base and a mounted robotic arm, with the two components typically controlled as separate subsystems. This is enabled by the fact that most mobile bases with three or four-wheeled designs are inherently stable, though lacking in maneuverability. In contrast, dynamically stable mobile bases offer greater agility and safety in crowded human interaction scenarios, though requiring active balancing. In this work, we consider the balancing problem for a Two-Wheeled Inverted Pendulum Mobile Manipulator (TWIP-MM), designed for retail shelf inspection. Using deep reinforcement learning methods (PPO and SAC), we can generate whole-body control strategies that leverage the motion of the robotic arm for in-place stabilization of the base, through a completely model-free approach. In contrast, tuning a standard PID controller requires a model of the robot, and is considered here as a baseline. Compared to PID control in simulation, the RL-based controllers are found to be more robust against changes in initial conditions, variations in inertial parameters, and disturbances applied to the robot.

Keywords: Cooperative control, Multivehicle systems, Autonomous systems
Abstract: This paper proposes an algorithm for decentralized adaptive coverage control of a heterogeneous group of agents in a convex environment. The kinematics of each agent can be described by either a single integrator, a double integrator, or a unicycle. The function defining the relative importance of points in the environment is not known to the agents, and an adaptation law is used by the agents to learn about the relative importance over time. A Lyapunov based stability and convergence proof is provided for the proposed algorithm and it is verified through several relevant simulations.

Keywords: Linear systems, Control education
Abstract: This paper discusses about the step response of linear time-invariant systems (continuous and discrete) for the identification of the presence of initial undershoot. The relation between Markov parameters and presence of initial undershoot is explored and methods are proposed accordingly on how the identification can be done employing these parameters. The viability and scope of these theorems are shown by considering examples based on practical applications that give arise to such characteristic in their step response curves. The calculated results are verified using MATLAB-based plots.

Keywords: Networked control systems, Control of networks, Control of communication networks
Abstract: This paper proposes a network-based event-triggered control for a linear continuous-time system. The primary feature of the proposed event-triggered mechanism is to trigger an event and transmit the system measurements when a pre-defined condition on input error is satisfied. Due to an input error in the triggered condition, redundant control updates are avoided, which can further decrease the number of events for some instances under a network resource-constrained environment. Moreover, a continuous-time dynamic event-triggered mechanism is suggested to improve resource utilization. Furthermore, a finite positive time interval between two consecutive events and the system’s stability are established. A numerical example is considered to show the effectiveness of the proposed work.

Keywords: Stochastic systems, Hybrid systems, Networked control systems
Abstract: In this paper, we study the dynamics of a linear feedback control system where control is effected via a sample-and-hold implementation of a state-feedback control law, with samples taken at the random event times of a renewal process. Our primary interest is in quantifying, using limit theorems of probability, fluctuations of the system with fast---but finite rate---sampling from its idealized continuously sampled counterpart. Exploiting the linearity and explicit solvability of the system in between samples, questions about the original continuous-time system can be studied through the investigation of an embedded discrete-time stochastic process. The latter records the system state at just the sampling instants, and can be represented in terms of a product of random matrices. We now use limit theorems of the Law of Large Numbers (LLN) and Central Limit Theorem (CLT) type for random matrix products to obtain information about the mean behavior and the typical fluctuations about the mean for the discrete-time process in the limit as the temporal sampling rate goes to infinity.

Keywords: Power systems, Cooperative control, Control of networks
Abstract: Distributed secondary control has been used as leading strategy to regulate the frequency and voltage of islanded AC microgrids, acting as cooperative multi-agent systems with droop controlled inverters. This paper considers the secondary control of an islanded microgrid as a leader-follower consensus problem, and implements a distributed finite-time strategy to restore the frequency of inverter-based generators, connected via detail-balanced directed topology. We show that the proposed controller restores the frequencies in the finite-time, while ensuring accurate real power-sharing among generators. We also provide an explicit expression for an upper bound on the convergence time. Simulations are given to illustrate the performance of the proposed controller. A comparison with undirected communication topology is also provided.

Keywords: Machine learning, Intelligent systems, Neural networks
Abstract: Cognitive cyber-physical system is a concept at the confluence of modern machine learning, neuro-cognitive sciences, and cyber-physical systems. The main goal of this talk is to present our vision for cognitive cyber-physical systems and discuss a research agenda that can realize them. We will begin with a brief historical view of cybernetics and explain how the concept of cognitive cyber-physical systems allows us to envision future cyber-physical systems integrated with machine learning and artificial intelligence. We will present key cognitive properties and how they might be realized in cognitive cyber-physical systems. We will present some of our preliminary work on this topic. The talk will conclude with a discussion of major research challenges for the future.

Keywords: Machine learning, Uncertain systems, Large scale systems
Abstract: By default, machine learned models are trained for deployment on data distributions that match the training distribution. As machine learning gets entrenched in our way of life, our models need to embrace the inevitability of change. Change comes in many different forms. Some changes are certain and the changed value is predictable --- for example, time of deployment. Surprisingly, even for such a predictable change current training objectives show suboptimal foresight. For other cases, the direction of change may be known during training, but the changed value is unknown. For handling temporal drift, we will discuss techniques such as continuous transportation of past data, kernel smoothed time-sensitive parameters, adversarial learning of time-invariant features, and special regularizers to control temporal complexity. For handling discrete shifts, we will discuss training strategies that view the training data as a mixture of groups to promote shared and generalizable features in various ways.

Keywords: Spacecraft control, Aerospace
Abstract: Design of a closed loop guidance algorithm gets complicated as thrust from the propulsion system decreases considerably. Some of the assumptions made during the guidance algorithm design for an impulsive orbit transfer becomes invalid in case of a low acceleration system where the orbit transfer is achieved by means of a long duration burn. The long duration burn results in considerable loss of energy due to gravity/arc losses. Also in case of an elliptical to circular orbit transfer, the algorithm is very sensitive to its ignition point and a wrong ignition point manifests as severe eccentricity in the achieved orbit and excessive fuel consumption as well. This paper proposes a simple yet effective velocity based Gravity Compensated Long Duration (GCLD) Orbit Transfer guidance algorithm that accounts for the gravity/arc losses during the thrusting phase. The proposed algorithm caters for in-plane and out-of-plane requirements and thereby meets the targeted orbital conditions with minimal deviations. The paper addresses the difficulty of encountering inclination correction at points near the anti-node and it also proposes a kinematic condition based adaptive ignition logic which ensures that the targeted orbital conditions are achieved with reduced fuel consumption.

Keywords: Aerospace, Control applications
Abstract: In this paper, terminal sliding mode control based impact time-constrained guidance strategies are proposed, which enable the pursuers to achieve individual homing based simultaneous interception of a stationary target. Guidance commands are derived using switching surfaces based on range errors and their rates. As the guidance laws are designed using nonlinear engagement kinematics, the proposed strategies achieve salvo interception at desired impact time even for the engagement with large heading angle errors. Unlike most of the existing guidance strategies, the proposed guidance strategies circumvent the possible degradations due to erroneous time-to-go estimates. The proposed strategies are shown to perform satisfactorily for different impact times and also exhibited desirable terminal features as compared to existing salvo strategies.

Keywords: Optimal control, Spacecraft control, Linear systems
Abstract: A robust guidance algorithm for docking with a target satellite in Low Earth Orbit is proposed in this work. An optimal control logic-based design minimizes the fuel consumption thereby maximizing the payload. A linear quadratic integral controller that can tackle model error as well as deviations from desired initial conditions that must be attained before initiation of docking procedures is designed. Practical considerations such as thruster capability are accounted for. An approach facilitating soft docking as well as one which gives non-oscillatory results are considered separately and compared. The designed controller is tested against a variety of initial conditions and disturbances. The guidance algorithm can easily be interfaced with machine-friendly languages like C or Python.

Keywords: Aerospace, Control applications, Cooperative control
Abstract: This paper presents predefined-time consensus-based cooperative guidance laws for a swarm of interceptors to simultaneously capture a non-maneuvering target. Unlike leader-follower cooperative guidance techniques, we design laws for a swarm of interceptors that has no leader and each interceptor executes its own distributed cooperative guidance command. This obviates the residency of the mission over a single interceptor. First, we present the cooperative guidance command against a stationary target, and extend the proposed design using two different approaches for simultaneous interception of a target moving with constant speed. Rigorously, we show that the proposed cooperative guidance laws guarantee consensus in the interceptors' time-to-go values within a predefined-time. The proposed design allows a feasible time of consensus in time-to-go to be set arbitrarily at will during the design regardless of the interceptors' initial time-to-go values, thereby ensuring a simultaneous interception in various engagement scenarios. We also demonstrate the efficacy of the proposed design via simulations.

Keywords: Cooperative control, Multivehicle systems, Networked control systems
Abstract: This paper studies the formation control of a multi-agent system where each agent is considered to have a physical shape, unlike a point mass model representation. For simplicity, we consider that the shape of each agent is characterized by a circular disk of the same radii. Leveraging the inter-center distance or interior-angle information among the neighboring agents, that can be easily measured by low-cost vision sensors, we apply constraint on the distance between the two agents such that they avoid collisions as well as maintain connectivity with the neighboring agents. To achieve these constraints on inter-agent distances, we exploit the idea of asymmetric barrier Lyapunov function from the existing literature, and design the stabilizing control law. We show that the agents asymptotically converge to the desired formation and their distances follow the required constraints. Simulations are provided to illustrate the efficacy of the proposed control law.

Keywords: Cooperative control, Machine learning, Modeling and simulation
Abstract: The control settings of a turbines play a major role in increasing the energy production from a wind farm. The nonlinear interactions of wake between the turbines make optimal control of wind farm a challenging task. Therefore, it’s hard to find the proper model based method to optimize the control settings. In the recent years, Reinforcement Learning (RL) has been emerging as a promising method for wind farm control. However, its efficacy is not evaluated when compared with nonlinear control strategies. In this study, yaw misalignment is used as control parameter to deflect the wakes and increase the power production from a 44 wind farm. A model-free Deep Deterministic Policy Gradient (DDPG) method and model-based iterative Linear Quadratic Regulator (iLQR) based Reinforcement Learning Techniques are utilized to optimize the yaw misalignments. To prove the efficiency of RL techniques, the results of DDPG and iLQR are compared with a nonlinear cooperative control strategy, Maximum Power Point Tracking solved through gradient based optimization approach.

Keywords: Modeling and simulation, Machine learning, Systems biology
Abstract: Process optimization and scale up for biomolecules/vaccine production remain challenging due to the adaptation of experiment based route which needs a large number of expensive experiments making it more challenging in translating the compound for industrial production. In this context, we propose a framework amalgamating systems biology and artificial intelligence for control and optimization of the protein/vaccine production in a Baculovirus expression system [BEVs]. Experimental investigation is conducted to study the growth of insect cells (Sf-9) when infected with the wild type Baculovirus (AcMNPV). Optimal unstructured model replicating the experimental data on cell and virus growth has been identified using a computation strategy consisting of a hybrid optimization technique. The selected model is then used for large scale data generation with an objective to build AI based RNN model that can be proved extremely helpful to handle numerical stability related issues while performing optimal control of the biological system. This work shows a proof of concept and represents the first instance, where an experimental study, mathematical modeling and AI based techniques have been applied for optimal protein production in recombinant expression system at industry setting.

Keywords: Optimization, Optimization algorithms
Abstract: Peer-to-Peer (P2P) energy trading is the direct sharing of energy between the grid-connected users. An efficient P2P energy trading platform paves the way for sustainable development since it encourages more generation from renewables locally. Setting up a new P2P platform and bringing that to a successful one is challenging due to technical, economic and social factors. In this paper, we focus on the economic aspect of this challenge. We propose a novel model of P2P trading by which a policymaker can choose whether to encourage more local generation or consumption. We model the P2P energy trading as a single leader multiple follower Stackelberg game with the auctioneer or the policymaker as the single leader, and the prosumers (producer + consumer) as the followers. Depending on the bids submitted by the sellers (producers) and buyers (consumers), the auctioneer using double auction determines the winners for trading. For the winners, the auctioneer fixes a price maximizing the average social welfare of prosumers, and the prosumers decide their quantities maximizing their welfare functions. We show the existence and uniqueness of Stackelberg equilibrium in such a scenario. We also propose an algorithm to find the Stackelberg equilibrium price and quantities. We consider different test cases to analyze the existence of the Stackelberg equilibrium and the effect of the equilibrium on P2P energy trading.

Keywords: Nonlinear systems, Modeling and simulation, Power systems
Abstract: This manuscript presents a reduced-order modeling framework that preserves the structure of nonlinear power system models. The offline reduced manifold is formed using the second-order nonlinear moment-matching (SO-NLMM) technique. A hyper-reduction of the nonlinear inner-products is then performed utilizing the discrete empirical interpolation method (DEIM). The overall scheme is used to obtain nonlinear reduced models for large-scale power system models. The results present a significant saving in the CPU times while preserving the second-order structure of the original model.

Keywords: Modeling and simulation, Algebraic/geometric methods, Nonlinear systems
Abstract: The dynamics of an inverted pendulum naturally evolves on the nonlinear manifold S^1. The paper proposes the modeling of the dynamics of an inverted pendulum on the nonlinear manifold S^1. The paper also proposes a variational integrator for the dynamics of the inverted pendulum directly on S^1. The variational integration results in the conservation of configuration space as well as energy as compared to Runge-Kutta methods which destroys the configuration space S^1 and is not able to conserve the energy. A control law is also proposed on S^1 to stabilize the pendulum at a given reference configuration. These are illustrated with numerical simulation and comparison results in the paper.

Keywords: Chaotic systems, Observers for nonlinear systems, Estimation
Abstract: This work considers the problem of chaos synchronization and parameter estimation, for the special case where the unknown parameters are linearly injected into the system. This case is of particular interest because scalar parameters often appear in systems with hidden attractors. For this type of system, state and parameter estimation can be achieved simultaneously by appropriately rewriting the system into descriptor form, and designing an observer that estimates the augmented system’s state. The design is adapted to achieve anti-synchronization as well, and a unified switching observer is proposed that can achieve both synchronization and anti-synchronization, based on the values of a switching signal. The design is showcased through an example of a modified chaotic system with hidden, coexisting attractors.

Keywords: Nonlinear systems, Emerging control applications, Learning
Abstract: Convergent Cross Mapping (CCM) was introduced as a data-driven technique to identify causal links in weakly coupled deterministic non-linear systems where other causal definitions, like the celebrated Granger Causality, fail due to their limited applicability to stochastic systems only. CCM is based on the idea of quantifying the extent to which a potential causal signal x[k] is recoverable from another effect signal y[k] with increasing data length. A major drawback of the CCM is its inability to distinguish between direct and indirect causal links that is necessary for reconstructing the direct causal network from observed time series. In this work, we propose a multivariable approach to solve this issue. First, we perform the pair-wise CCM analysis and identify all the effects (both direct and indirect) linked to a cause. Next, we perform a multivariable state-space reconstruction using the identified effect variables and use it to recover the cause variable. We then evaluate the incremental improvement in the recovery as compared to the univariable case. A significant improvement indicates that the effect is an indirect one, while the converse indicates a direct effect. We also address a second shortcoming of CCM by proposing an improved metric for quantifying cross mapping of variables. Case studies on simulated and real data sets are presented to demonstrate the success of proposed developments.

Keywords: Switched systems, Learning, Automata
Abstract: We propose an automata theoretic learning algorithm for the identification of black-box switched linear systems whose switching logics are event-driven. A switched system is expressed by a deterministic finite automaton (FA) whose node labels are the subsystem matrices. With information about the dimensions of the matrices and the set of events, and with access to two oracles, that can simulate the system on a given input, and provide counter-examples when given an incorrect hypothesis automaton, we provide an algorithm that outputs the unknown FA. Our algorithm first uses the oracle to obtain the node labels of the system run on a given input sequence of events, and then extends Angluin's (L^*)-algorithm to determine the FA that accepts the language of the given FA. We demonstrate our learning algorithm on a numerical example.

Keywords: Robust control, Output feedback, Optimal control
Abstract: A problem of designing dynamic output feedback robust controller for LTI systems is considered. The reduced order controller design aims to guarantee a minimum bound in terms of disturbance attenuation performance. For a finite-time interval, the designed min-max controller attenuates the effect of worst case external disturbances and bounds the system trajectories to a predefined set, over all possible initial conditions. Sufficient conditions for the existence of such controller are formulated using differential matrix inequalities and the upper bound on the cost function can be minimized using the proposed algorithm.

Keywords: Direct adaptive control, Indirect adaptive control, Robust adaptive control
Abstract: This paper aims to compare the performance of Direct Adaptive Inverse Control (DAIC) and Indirect Adaptive Inverse Control (IAIC) applied to a non-minimum phase plant in the presence of a periodic disturbance signal added to the control signal. Besides the structural differences, the performance of DAIC and IAIC is influenced, during the update of the estimate of the controller weights vector, by the convergence speed and steady-state Mean Square Error (MSE). Thus, in this work a new adaptive algorithm based on stochastic gradient, entitled Fuzzy Variable Step Size Normalized Least Mean Square (FVSS-NLMS), is proposed. In the FVSS-NLMS algorithm, a Mamdani Fuzzy Inference System (MFIS) is used to adapt the step size of NLMS algorithm, with the objective of obtain a good performance in terms of convergence speed and steady-state MSE. The results obtained by the DAIC and IAC designed by the FVSS-NLMS algorithm were compared with versions of NLMS algorithm with fixed and variable step size.